Nuprl Lemma : es-interval-induction
∀es:EO. ∀i:Id.
∀[P:e1:{e:E| loc(e) = i ∈ Id} ─→ {e2:E| loc(e2) = i ∈ Id} ─→ ℙ]
(∀e1@i.∀e2≥e1.(∀e:E. ((e1 <loc e) ⇒ e ≤loc e2 ⇒ P[e;e2])) ⇒ P[e1;e2] ⇒ ∀e1@i.∀e2≥e1.P[e1;e2])
Proof
Definitions occuring in Statement :
alle-ge: ∀e'≥e.P[e'],
alle-at: ∀e@i.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
alle-at_wf,
all_wf,
es-le_wf,
es-locl_wf,
es-le-loc,
es-E_wf,
Id_wf,
es-loc_wf,
event_ordering_wf,
le_wf,
length_wf,
es-interval_wf,
subtract_wf,
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
equal_wf,
es-le-self,
member-es-interval,
non_neg_length,
length_wf_nat,
length_zero,
member-implies-null-eq-bfalse,
and_wf,
list_wf,
null_wf3,
subtype_rel_list,
top_wf,
null_nil_lemma,
btrue_wf,
btrue_neq_bfalse,
es-interval-partition,
length-append,
es-le-pred,
es-locl-first,
assert_elim,
assert_wf,
es-first_wf2,
es-interval-non-zero,
es-pred_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:e1:\{e:E| loc(e) = i\} {}\mrightarrow{} \{e2:E| loc(e2) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e1@i.\mforall{}e2\mgeq{}e1.(\mforall{}e:E. ((e1 <loc e) {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} P[e;e2])) {}\mRightarrow{} P[e1;e2]
{}\mRightarrow{} \mforall{}e1@i.\mforall{}e2\mgeq{}e1.P[e1;e2])
Date html generated:
2015_07_17-AM-08_51_20
Last ObjectModification:
2015_01_27-PM-01_20_16
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